Applied Statistics Model Question Paper

12th Standard EM

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Business Maths

Time : 02:00:00 Hrs
Total Marks : 60
    10 x 1 = 10
  1. A time series is a set of data recorded

    (a)

    Periodically

    (b)

    Weekly

    (c)

    successive points of time

    (d)

    all the above

  2. The value of ‘b’ in the trend line y=a+bx is

    (a)

    Always positive

    (b)

    Always negative

    (c)

    Either positive or negative

    (d)

    Zero

  3. Another name of consumer’s price index number is:

    (a)

    Whole-sale price index number

    (b)

    Cost of living index

    (c)

    Sensitive

    (d)

    Composite

  4. Laspeyre’s index = 110, Paasche’s index = 108, then Fisher’s Ideal index is equal to:

    (a)

    110

    (b)

    108

    (c)

    100

    (d)

    109

  5. While computing a weighted index, the current period quantities are used in the:

    (a)

    Laspeyre’s method

    (b)

    Paasche’s method

    (c)

    Marshall Edgeworth method

    (d)

    Fisher’s ideal method

  6. How many causes of variation will affect the quality of a product?

    (a)

    4

    (b)

    3

    (c)

    2

    (d)

    1

  7. The assignable causes can occur due to

    (a)

    poor raw materials

    (b)

    unskilled labour

    (c)

    faulty machines

    (d)

    all of them

  8. \(\overset {-}{X}\)chart is a

    (a)

    attribute control chart

    (b)

    variable control chart

    (c)

    neither Attribute nor variable control chart

    (d)

    both Attribute and variable control chart

  9. R is calculated using

    (a)

    xmax-xmin

    (b)

    xmin-xmax

    (c)

    \(\overset{-}{x}\)max-\(\overset{-}{x}\)min

    (d)

    \(\overset{=}{x}\)max-\(\overset{=}{x}\)min

  10. The LCL for R chart is given by

    (a)

    \({ D }_{ 2 }\bar { R } \)

    (b)

    \({ D }_{ 2 }\overset { = }{ R } \)

    (c)

    \({ D }_{ 3 }\overset { = }{ R } \)

    (d)

    \({ D }_{ 3 }\bar { R } \)

  11. 10 x 2 = 20
  12. Define Time series.

  13. State the uses of time series.

  14. Define secular trend.

  15. Define seasonal index.

  16. State the different methods of measuring trend.

  17. Determine the equation of a straight line which best fits the following data

    Year 2000 2001 2002 2003 2004
    Sales(Rs.'000) 35 36 79 80 40

    Compute the trend values for all years from 2000 to 2004

  18. The following table shows the number of salesmen working for a certain concern:

    Year 1992 1993 1994 1995 1996
    No. of salesmen 46 48 42 56 52

    Use the method of least squares to fit a straight line and estimate the number of salesmen in 1997.

  19. State the uses of Index Number.

  20. Write note on Fisher’s price index number

  21. Define true value ratio.

  22. 5 x 3 = 15
  23. Fit a trend line by the method of semi-averages for the given data.

    Year 1990 1991 1992 1993 1994 1995 1996 1997
    Sales 15 11 20 10 15 25 35 30
  24. Calculate four-yearly moving averages of number of students studying in a higher secondary school in a particular city from the following data.

    Year 2001 2002 2003 2004 2005 2006 2007 2008
    Sales 124 120 135 140 145 158 162 170
  25. Given below are the data relating to the sales of a product in a district.
    Fit a straight line trend by the method of least squares and tabulate the trend values.

    Year 1995 1996 1997 1998 1999 2000 2001 2002
    Sales 6.7 5.3 4.3 6.1 5.6 7.9 5.8 6.1
  26. A machine drills hole in a pipe with a mean diameter of 0.532 cm and a standard deviation of 0.002 cm. Calculate the control limits for mean of samples 5.

  27. The following data gives readings of 10 samples of size 6 each in the production of a certain product. Draw control chart for mean and range with its control limits.

    Sample 1 2 3 4 5 6 7 8 9 10
    Mean 383 508 505 582 557 337 514 614 707 753
    Range 95 128 100 91 68 65 148 28 37 80
  28. 3 x 5 = 15
  29. the Laspeyre’s, Paasche’s and Fisher’s price index number for the following data. Interpret on the data.

    Commodities Price Quandity
    2000 2010 2000 2010
    Rice 38 35 6 7
    Wheat 12 18 7 10
    Rent 10 15 10 15
    Fuel 25 30 12 16
    Miscellaneous 30 33 8 10
  30. Calculate the cost of living index number for the year 2015 with respect to base year 2010 of the following data.

    Commodities Number of
    Units
    (2010)
    Price
    (2010)
    Price
    (2015)
    Rice 5 1500 1750
    Sugar 3.5 1100 1200
    Pulses 3 800 950
    Cloth 2 1200 1550
    Ghee 0.75 550 700
    Rent 12 2500 3000
    Fuel 8 750 600
    Misc 110 3200 3500
  31. Construct the cost of living index number for 2011 on the basis of 2007 from the given data using family budget method.

    Commodities Price Weights
    2007 2011
    A 350 400 40
    B 175 250 35
    C 100 115 15
    D 75 105 20
    E 60 80 25

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